cp's OEIS Frontend

A247520 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.

%I A247520 #9 Sep 26 2014 21:11:51
%S A247520 2,8,13,17,22,26,30,33,41,43,46,48,55,61,63,69,74,79,83,92,99,103,108,
%T A247520 111,115,118,125,127,133,138,144,148,153,156,158,165,170,172,176,181,
%U A247520 184,187,189,198,204,207,212,214,216,221,227,229,235,242,248,250
%N A247520 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
%C A247520 Every positive integer lies in exactly one of these: A247519, A247520, A247521, A247522.
%H A247520 Clark Kimberling, <a href="/A247520/b247520.txt">Table of n, a(n) for n = 1..1000</a>
%e A247520 r has binary digits 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, ...
%e A247520 s has binary digits 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, ...
%e A247520 so that a(1) = 2.
%t A247520 z = 400; r1 = GoldenRatio; r = FractionalPart[r1]; s = FractionalPart[r1/2];
%t A247520 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
%t A247520 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
%t A247520 t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247520 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247520 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247520 t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247520 Flatten[Position[t1, 1]] (* A247519 *)
%t A247520 Flatten[Position[t2, 1]] (* A247520 *)
%t A247520 Flatten[Position[t3, 1]] (* A247521 *)
%t A247520 Flatten[Position[t4, 1]] (* A247522 *)
%Y A247520 Cf. A247519, A247521, A247522.
%K A247520 nonn,easy,base
%O A247520 1,1
%A A247520 _Clark Kimberling_, Sep 19 2014